18.10: Statically Indeterminate Problem Solving
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining equilibrium, leading to a surplus of unknown reactions over the available equilibrium equations.
The statical indeterminacy is resolved by considering the reaction at point C as redundant and releasing it from its support. This redundant reaction is treated as an additional load. The superposition method is then deployed to determine the deformation in each section of the rod structure. By combining these individual deformations, the total deformation expression for the entire structure is derived. Considering the expressions, the total deformation of the rod structure equals zero, and the summation of all the loads equals zero, the unknown reaction forces are determined. Finally, the deflection at point B is calculated by summing the deformations in the rod structure sections preceding point B.
